Proof.
Note that \(\begin{bmatrix} \!\!\! \otimes ^t A & \otimes ^t B \\ \otimes ^t B^* & \otimes ^t C \end{bmatrix}\) 
is positive semidefinite.
By restricting this block matrix to
the symmetric class of tensor product (see, e.g., [1]}), we know that
\( \begin{bmatrix} \!\!\! \vee ^t A & \vee ^t B \\ \vee ^t B^* & \vee ^t C \end{bmatrix} \) 
